Nonlinear Markov processes and kinetic equations

"A nonlinear Markov evolution is a dynamical system generated by a measure-valued ordinary differential equation with the specific feature of preserving positivity. This feature distinguishes it from general vector-valued differential equations and yields a natural link with probablity, both in interpreting results and in the tools of analysis." "This cutting-edge book, the first devoted to the area, develops this interplay between probability and analysis. After systematically presenting both analytic and probabilistic techniques, the author uses probability to obtain deeper insight into nonlinear dynamics, and analysis to tackle difficult problems in the description of random and chaotic behavior. The book addresses the most fundamental questions in the theory of nonlinear Markov processes: existence, uniqueness, constructions, approximation schemes, regularity, law of large numbers, and probabilistic interpretations. Its careful exposition makes the book accessible to researchers and graduate students in stochastic and funtional analysis, with applications to mathematical physics and systems biology." "This series is devoted to thorough, yet reasonably concise, treatments of topics in any branch of mathematics. Typically, a Tract takes up a single thread in a wide subject, and follows its ramifications, thus throwing light on its various aspects. Tracts are expected to be rigorous, definitive, and of lasting value to mathematicians working in the relevant disciplines. Exercises can be included to illustrate techniques, summarize past work, and enhance the book's value as a seminar text. All volumes are properly edited and typeset, and are published, initially at least, in hardback."--Jacket.